x + xy + y? = 9 %3D sa slanted ellipse illustrated in this figure: 1 – 4 -2 2.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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x? + xy + y? = 9
is a slanted ellipse illustrated in this figure:
2
1
-2
-1
-2
Think of
y as a function of x. Differentiating implicitly and solving for y' gives:
(Your answer will depend on x and y.) The ellipse has two horizontal tangents. The upper one has the equation
y =
The right most vertical tangent has the equation
That tangent touches the ellipse where
Hint: The horizontal tangent is of course characterized by y'
implicitly, solve for x' and then set x' = 0.
0. To find the vertical tangent use symmetry, or think of x as a function of y, differentiate
=
Transcribed Image Text:x? + xy + y? = 9 is a slanted ellipse illustrated in this figure: 2 1 -2 -1 -2 Think of y as a function of x. Differentiating implicitly and solving for y' gives: (Your answer will depend on x and y.) The ellipse has two horizontal tangents. The upper one has the equation y = The right most vertical tangent has the equation That tangent touches the ellipse where Hint: The horizontal tangent is of course characterized by y' implicitly, solve for x' and then set x' = 0. 0. To find the vertical tangent use symmetry, or think of x as a function of y, differentiate =
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